Technical Field
The disclosure relates to a micro-electro mechanical apparatus. Particularly, the disclosure relates to a micro-electro mechanical apparatus with interdigitated spring.
Related Art
In recent years, with the development of electronic products such as smart phones, tablet PCs, game consoles, etc., micro-electro mechanical inertial sensors such as accelerometers, gyroscopes, oscillators, etc. are widely used in the aforementioned electronic products. The market for these products has significantly increased each year. Currently, techniques of the micro-electro mechanical inertial sensors have gradually matured, and the miniaturization, high on-axis sensitivity, low off-axis sensitivity and high process variation tolerance have become competitive factors in the current micro-electro mechanical inertial sensors market.
However, when a mass of the current micro-electro mechanical inertial sensor is miniaturized, a conventional spring is proportionally scaled-down in a same manner, such that stiffness of the conventional spring is excessively high. This decreases accuracy and sensitivity. Moreover, when the mass of the micro-electro mechanical inertial sensor is miniaturized, a more precise fabrication process is adopted to fabricate the conventional spring. Thus, a width of the conventional spring becomes smaller, which decreases the tolerance of fabricating error, and induces larger resonance frequency drift.
FIG. 1A is a schematic diagram of a micro-electro mechanical accelerometer. FIG. 1B is a schematic diagram of the micro-electro mechanical accelerometer of FIG. 1A with a miniaturized mass. Referring to FIG. 1A, the micro-electro mechanical accelerometer 10 includes a mass 12, springs 14 and sensing electrodes 16, where stiffness of the spring 14 is K. Each of the sensing electrodes 16 includes a stationary electrode 16a and a movable electrode 16b. When acceleration is applied along an X-axis direction, the mass 12 translates along the X-axis direction, and the distance between the stationary electrode 16a and the movable electrode 16b is changed to cause a capacitance variation. By sensing the capacitance variation, the acceleration can be calculated.
Then, referring to FIG. 1B, the micro-electro mechanical accelerometer 20 includes a mass 22, springs 24 and sensing electrodes 26, where stiffness of the spring 24 is k. Each of the sensing electrodes 26 includes a stationary electrode 26a and a movable electrode 26b. 
In the micro-electro mechanical accelerometer, when the mass is scaled-down, it is difficult to reduce the stiffness of the spring. When the stiffness of the spring is excessively high, the displacement along a sensing axis is decreased. This is detrimental for sensing small acceleration and decreases the sensitivity of the accelerometer. When the stiffness of the spring is excessively low, the off-axis acceleration increases the displacement along the sensing axis which decreases the accuracy. In order to keep the same sensitivity, the same displacement should be maintained when the dimension of the accelerometer is scaled down. For example, when the side length L2 in FIG. 1B is one half of the side length L1 in FIG. 1A, the stiffness of the spring 24 of the mass 22 has to be decreased to one quarter of the stiffness of the spring 14 of the mass 12. It can be found in the following equation.
  {          ⁢                                                        F              =                                                M                  ·                  g                                =                                  K                  ⁢                                                                          ⁢                  Δ                  ⁢                                                                          ⁢                  y                                                                                                        f              =                                                m                  ·                  g                                =                                                      (                                                                  1                        4                                            ⁢                      M                                        )                                    ·                  g                                                                                                                                                    ⁢                              =                                                                            1                      4                                        ⁢                                          M                      ·                      g                                                        =                                                                                    1                        4                                            ⁢                      K                      ⁢                                                                                          ⁢                      Δ                      ⁢                                                                                          ⁢                      y                                        =                                          k                      ⁢                                                                                          ⁢                      Δ                      ⁢                                                                                          ⁢                      y                                                                                                              ⁢                          ⇒      k        =                  1        4            ⁢      K      
In the above equation, F is a force applied on mass 12, f is a force applied on mass 22, M is a mass of mass 12, m is a mass of mass 22, and Δy is a displacement of mass 12.
FIG. 2A is a schematic diagram of a micro-electro mechanical resonator. FIG. 2B is a schematic diagram of the miniaturized micro-electro mechanical resonator according to FIG. 2A. Referring to FIG. 2A, the micro-electro mechanical resonator 30 includes a mass 32, springs 34, sensing electrodes 36 and driving electrodes 38. Each sensing electrode 36 includes a stationary electrode 36a and a movable electrode 36b. Each driving electrode 38 includes a stationary electrode 38a and a movable electrode 38b. The mass 32 is driven by the electrode 38 to oscillate. When the mass 32 reaches a resonance frequency, the mass 32 has a maximum displacement, and the sensing electrode 36 senses a maximum capacitance variation.
Referring to FIG. 2B, the micro-electro mechanical resonator 30′ includes a mass 32′, springs 34′, sensing electrodes 36′ and driving electrodes 38′. Each sensing electrode 36′ includes a stationary electrode 36′a and a movable electrode 36′b. Each driving electrode 38′ includes a stationary electrode 38′a and a movable electrode 38′b. When the micro-electro mechanical resonator 30 is miniaturized to the micro-electro mechanical resonator 30′, the width of the spring 34 has to be accordingly narrowed so that the miniaturized micro-electro mechanical resonator 30′ can achieve the same resonance frequency as that of the micro-electro mechanical resonator 30. The narrowed spring width can be obtained according to a following equation (3) by substituting an equation (1) into an equation (2):
                    k        =                                            n              p                                                      n                s                            .                                ·          E          ·          t          ·                                    (                              w                L                            )                        3                                              (        1        )                                f        =                              1                          2              ⁢                                                          ⁢              π                                ⁢                                    k              m                                                          (        2        )                                w        =                  L          ·                                    [                                                                    n                    s                                                        n                    p                                                  ·                                                      4                    ⁢                                                                                  ⁢                                                                  π                        2                                            ·                                              f                        2                                            ·                      m                                                                            E                    ·                    t                                                              ]                                      1              /              3                                                          (        3        )            
where f is the resonance frequency, k is the stiffness of the folded spring, m is a mass value of the mass, np is a number of folded springs disposed at a same side, ns is a number of folded portions of each folded spring, E is a Young's modulus of the folded spring, t is a thickness of the folded spring, w is a width of the folded spring and L is a length of the folded spring.
Under the same fabrication process variation (for example, variation of width), the effect on the spring with a narrower width is greater than that on the spring with a wider width. The spring with the narrower width results in the micro-electro mechanical resonator 30′ having a larger frequency drift. More precisely, there is a large difference between a designed resonance frequency and a measured resonance frequency of the micro-electro mechanical resonator 30′.
FIG. 3 is a schematic diagram of a micro-electro mechanical gyroscope. Referring to FIG. 3, the micro-electro mechanical gyroscope 40 includes an accelerometer 50 and a resonator 60. The accelerometer 50 includes a first mass 52. The resonator 60 includes a second mass 62. When the second mass 62 oscillates along a Y-axis at resonance frequency, the first mass 52 is driven to oscillate along the Y-axis. When an angular velocity is applied along a Z-axis, the first mass 52 translates along the X-axis, and a distance between a movable electrode 52b on the first mass 52 and a stationary electrode on a substrate SUB 1 is changed. This causes a capacitance variation. Then, by sensing the capacitance variation, the magnitude of the angular velocity can be calculated. However, when the accelerometer 50 is miniaturized, sensitivity and accuracy of the accelerometer 50 are decreased, and when the resonator 60 is miniaturized, the resonator 60 may have larger frequency drift.
According to the aforementioned examples, it is known that “how to miniaturize the micro-electro mechanical inertia sensors such as an accelerometer, resonator, or gyroscope” has become a critical issue in the development of micro-electro mechanical inertial sensors. That is to say, for the purpose of miniaturizing the micro-electro mechanical inertial sensors, a spring with a wider width and lower stiffness on a sensing axis is required to match the miniaturized micro-electro mechanical inertia sensors.
FIG. 4 is a schematic diagram of an electromagnetically driven vibrating accelerometer. Referring to FIG. 4, it discloses an electromagnetically driven vibrating accelerometer 70, in which a mass 74 vibrates when an electric current passes through a driving spring 72. When the acceleration is sensed, the vibration frequency of the mass 74 is changed. Then, by detecting the variation of the vibration frequency, the magnitude of the acceleration can be calculated.
FIG. 5 is a schematic diagram of a micromechanical semiconductor device. Referring to FIG. 5, it discloses a micromechanical semiconductor device 80, in which a spring 82 has lower stiffness along a vertical direction (a Z-axis direction), such that a mass 84 is capable of moving vertically along the Z-axis direction.
FIG. 6 is a schematic diagram of a semiconductor physical quantity sensor. Referring to FIG. 6, it discloses a semiconductor physical quantity sensor 90, in which a bridge 92 is respectively connected to a connecting portion 94a of an inner spring 94 and a connecting portion 96a of an outer spring 96 to suppress the influence of the off-axis acceleration.